This is not difficult to accomplish, The <Flatlist/>
component already have methods to do that.
I have created a simple demo for you: https://snack.expo.io/@abranhe/flatlist-scroll
I have created a custom <Button/>
and <Card/>
components. I am creating an array with some random data with this format
const data = [
{ message: 'Random Message' }, { message: 'Random Message' }
]
I am adding a reference to the <Flatlist/>
by adding
ref={ref => (this.flatlist = ref)}
Then I call the methods and that's it.
<Button title="▼" onPress={() => this.flatlist.scrollToEnd()} />

The whole source code:
import React from 'react';
import { Text, View, FlatList, StyleSheet } from 'react-native';
import { random } from 'merry-christmas';
import Card from './components/Card';
import Button from './components/Button';
const data = [...Array(10)].map(i => ({ message: random() }));
export default () => (
<View style={styles.container}>
<FlatList
ref={ref => (this.flatlist = ref)}
data={data}
renderItem={({ item }) => <Card gretting={item.message} />}
/>
<View style={styles.bottomContainer}>
<Button
title="▲"
onPress={() => this.flatlist.scrollToIndex({ index: 0 })}
/>
<Button title="▼" onPress={() => this.flatlist.scrollToEnd()} />
</View>
</View>
);